Advanced Regression

This subject extends the use of regression methods in biostatistics to include the analysis of frequency counts and event rates. Generalised Linear Models (GLMs) are proposed as tools for description, prediction and causal inference in health research. Students will learn how to propose, fit and interpret Poisson regression models for counts and rates, and Cox’s proportional hazards model for time-to-event data with right censoring. The Kaplan-Meier and Mantel-Cox estimators and the log-rank test for the survival function given lifetime data will be discussed alongside regression methods for the analysis of survival data. Mathematical concepts covered include maximum likelihood estimation, the likelihood ratio test for model comparison and how GLMs provide a unifying theory for the analysis of the frequency of events occurring over time using logistic, Poisson and Cox regression.